Optimal bounds on texture coefficients

Let w be the orientation distribution function of a polycrystalline aggregate of crystallites with symmetry gcrand with group of texture symmetry gtex. In this paper we obtain a "recipe" on how to derive optimal bounds on the texture coefficients Wlmnassociated with w. In particular, we find explicit bounds in the case in which gtexis a group with orthorhombic symmetry and gcris either a group with cubic symmetry or a group with hexagonal symmetry.